Solve for $x$ and $y$ using elimination. $\begin{align*}6x+5y &= -8 \\ -2x+y &= -8\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $3$ $\begin{align*}6x+5y &= -8\\ -6x+3y &= -24\end{align*}$ Add the top and bottom equations. $8y = -32$ Divide both sides by $8$ and reduce as necessary. $y = -4$ Substitute $-4$ for $y$ in the top equation. $6x+5( -4) = -8$ $6x-20 = -8$ $6x = 12$ $x = 2$ The solution is $\enspace x = 2, \enspace y = -4$.